3.9: Solve MultiStep Equations Involving Decimals
Let’s Think About It
Sam found a bunch of change under his bed. He has a pile of quarters, a pile of dimes and a pile of nickels. He has the same number of quarters, dimes and nickels. When he adds it all up, he has eight dollars and eighty cents. How many of each coin does Sam have?
In this lesson, you will learn to solve multistep equations involving decimals.
Guidance
Let’s first think about integers. Integers include positive whole numbers (1, 2, 3, 4, 5, . . .), their opposites (1, 2, 3, 4, 5, . . .), and zero. Integers are rational numbers. A rational number is any number that can be written as the ratio of two integers or you can think of this in fraction form. So, an integer such as 3, which can be written as the ratio
What are some other rational numbers?
A fraction, such as
A terminating decimal, such as 0.1, is also rational because it can be written as the ratio
A repeating decimal, such as
Let’s start by looking at solving equations involving decimals.
Solve for ‘
First, subtract the like terms on the left side of the equation.
Next, isolate the term with the variable,
Then, divide by 0.5 to solve for ‘
The answer is 8.
Guided Practice
Here is one for you to try on your own.
Solve for ‘
First you can see that we have parentheses in this equation. Apply the distributive property to the left side of the equation. Multiply each of the two numbers inside the parentheses by 0.1.
Next, solve as you would solve any twostep equation. To get
Then, to get
The answer is 9.
Examples
Example 1
First, to get
The answer is 7.
Example 2
First, solve as you would solve any twostep equation. To get
Next, to get ‘
The answer is 70.
Example 3
First, combine like terms on the left side of the equation.
Next, to get
Then, to get ‘
The answer is 2.
Follow Up
Remember Sam who found the change under his bed. He looked at the pile of nickels, dime, and quarters and noticed that he had the same number of each coin. When he added it up, he had a total of $8.80. He wants to know how many of each coin he has.
First, let ‘
Next, combine like terms.
Then, divide both sides by 0.4.
The answer is 22.
Sam has 22 of each type of coin.
Video Review
https://www.youtube.com/watch?v=MHACBubIBIY
Explore More
Solve each equation to find the value of the variable.

3.2n+6.5n=38.8 
0.2(3+p)=4.6 
0.09y−0.08y=1.2 
0.06x+0.05x=0.99 
0.09x=81 
0.6x+1=19 
9.05x=27.15 
0.16x+3=3.48 
2.3a+4=15.5 
2(a+4)+0.5a=23 
0.54y+0.16y+0.22y=3.68 
x0.6=0.8 
y0.25=9 
0.6x−0.5x+11=12.1 
0.26x+0.18x=−3.08
Decimal
In common use, a decimal refers to part of a whole number. The numbers to the left of a decimal point represent whole numbers, and each number to the right of a decimal point represents a fractional part of a power of onetenth. For instance: The decimal value 1.24 indicates 1 whole unit, 2 tenths, and 4 hundredths (commonly described as 24 hundredths).fraction
A fraction is a part of a whole. A fraction is written mathematically as one value on top of another, separated by a fraction bar. It is also called a rational number.Integer
The integers consist of all natural numbers, their opposites, and zero. Integers are numbers in the list ..., 3, 2, 1, 0, 1, 2, 3...rational number
A rational number is a number that can be expressed as the quotient of two integers, with the denominator not equal to zero.Repeating Decimal
A repeating decimal is a decimal number that ends with a group of digits that repeat indefinitely. 1.666... and 0.9898... are examples of repeating decimals.Terminating Decimal
A terminating decimal is a decimal number that ends. The decimal number 0.25 is an example of a terminating decimal.Image Attributions
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Description
Learning Objectives
In this concept, you will learn to solve multistep equations involving decimals.
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Date Created:
Dec 19, 2012Last Modified:
Aug 10, 2015Vocabulary
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